3,633 research outputs found
Blind Interference Alignment for Private Information Retrieval
Blind interference alignment (BIA) refers to interference alignment schemes
that are designed only based on channel coherence pattern knowledge at the
transmitters (the "blind" transmitters do not know the exact channel values).
Private information retrieval (PIR) refers to the problem where a user
retrieves one out of K messages from N non-communicating databases (each holds
all K messages) without revealing anything about the identity of the desired
message index to any individual database. In this paper, we identify an
intriguing connection between PIR and BIA. Inspired by this connection, we
characterize the information theoretic optimal download cost of PIR, when we
have K = 2 messages and the number of databases, N, is arbitrary
Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes
We propose three private information retrieval (PIR) protocols for
distributed storage systems (DSSs) where data is stored using an arbitrary
linear code. The first two protocols, named Protocol 1 and Protocol 2, achieve
privacy for the scenario with noncolluding nodes. Protocol 1 requires a file
size that is exponential in the number of files in the system, while Protocol 2
requires a file size that is independent of the number of files and is hence
simpler. We prove that, for certain linear codes, Protocol 1 achieves the
maximum distance separable (MDS) PIR capacity, i.e., the maximum PIR rate (the
ratio of the amount of retrieved stored data per unit of downloaded data) for a
DSS that uses an MDS code to store any given (finite and infinite) number of
files, and Protocol 2 achieves the asymptotic MDS-PIR capacity (with infinitely
large number of files in the DSS). In particular, we provide a necessary and a
sufficient condition for a code to achieve the MDS-PIR capacity with Protocols
1 and 2 and prove that cyclic codes, Reed-Muller (RM) codes, and a class of
distance-optimal local reconstruction codes achieve both the finite MDS-PIR
capacity (i.e., with any given number of files) and the asymptotic MDS-PIR
capacity with Protocols 1 and 2, respectively. Furthermore, we present a third
protocol, Protocol 3, for the scenario with multiple colluding nodes, which can
be seen as an improvement of a protocol recently introduced by Freij-Hollanti
et al.. Similar to the noncolluding case, we provide a necessary and a
sufficient condition to achieve the maximum possible PIR rate of Protocol 3.
Moreover, we provide a particular class of codes that is suitable for this
protocol and show that RM codes achieve the maximum possible PIR rate for the
protocol. For all three protocols, we present an algorithm to optimize their
PIR rates.Comment: This work is the extension of the work done in arXiv:1612.07084v2.
The current version introduces further refinement to the manuscript. Current
version will appear in the IEEE Transactions on Information Theor
Asymmetry Helps: Improved Private Information Retrieval Protocols for Distributed Storage
We consider private information retrieval (PIR) for distributed storage
systems (DSSs) with noncolluding nodes where data is stored using a non maximum
distance separable (MDS) linear code. It was recently shown that if data is
stored using a particular class of non-MDS linear codes, the MDS-PIR capacity,
i.e., the maximum possible PIR rate for MDS-coded DSSs, can be achieved. For
this class of codes, we prove that the PIR capacity is indeed equal to the
MDS-PIR capacity, giving the first family of non-MDS codes for which the PIR
capacity is known. For other codes, we provide asymmetric PIR protocols that
achieve a strictly larger PIR rate compared to existing symmetric PIR
protocols.Comment: To be presented at 2018 IEEE Information Theory Workshop (ITW'18).
See arXiv:1808.09018 for its extended versio
Efficient Recovery of a Shared Secret via Cooperation: Applications to SDMM and PIR
This work considers the problem of privately outsourcing the computation of a
matrix product over a finite field to helper servers. These
servers are considered to be honest but curious, i.e., they behave according to
the protocol but will try to deduce information about the user's data.
Furthermore, any set of up to servers is allowed to share their data.
Previous works considered this collusion a hindrance and the download cost of
the schemes increases with growing . We propose to utilize such linkage
between servers to the user's advantage by allowing servers to cooperate in the
computational task. This leads to a significant gain in the download cost for
the proposed schemes. The gain naturally comes at the cost of increased
communication load between the servers. Hence, the proposed cooperative scheme
can be understood as outsourcing both computational cost and communication
cost.
While the present work exemplifies the proposed server cooperation in the
case of a specific secure distributed matrix multiplication (SDMM) scheme, the
same idea applies to many other use cases as well. For instance, other SDMM
schemes as well as linear private information retrieval (PIR) as a special case
of SDMM are instantly covered.Comment: 10 pages, 2 figure
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